Given matrix

= x [x² – (x + y) (x + 2y)] – (x + y) [(x + 2y) (x) – (x + y)²] + (x + 2y) [(x + 2y)² – x (x + y)]

= x [x² – x² – 3xy – 2y²] – (x + y) [x² + 2xy – x² – 2xy – y²] + (x + 2y) [x² + 4xy + 4y² – x² – xy]

= x [-3xy – 2y²] – (x + y) [-y²] + (x + 2y) [3xy + 4y²]

= -3x²y – 2xy² + xy² + y³ +3x²y + 4xy² + 6xy² + 8y³

= 9y³ + 9xy²

= 9y² (x + y) … option (B)

Hence, option B satisfies.